Combine the chili powder, dried oregano, ground cumin, salt, and black pepper. Rub over the pork shoulder on both sides and place it in the slow cooker.
Add the remaining ingredients to the slow cooker.
Cover and cook on low for 7-8 hours or high for 6-7 hours.
Remove the pork and shred it with two forks. Return it to the slow cooker until close to serving time.
Spread the shredded carnitas on a rimmed baking sheet and place under the broiler for 2-3 minutes to brown. Watch carefully so that it doesn't burn. Return to the juices in the slow cooker if desired.
Video
Notes
Store leftovers in an airtight container in the fridge for 3-4 days or in the freezer for up to a month.